Determining Solutions of a Differential Equation
determine which functions are
solutions of the linear differential equation.
7. $x^2y'' - 2y = 0$
(a) $\frac{1}{x^2}$
(b) $x^2$
(c) $e^x$
(d) $e^{-x^2}$
Finding the Wronskian for a Set of Functions
find the Wronskian for the set of
functions.
26. $\{x, e^x, \sin x, \cos x\}$
Testing for Linear Independence
(a) verify that each solution satisfies the differential
equation, (b) test the set of solutions for linear
independence, and (c) if the set is linearly independent,
then write the general solution of the differential equation.
Differential Equation
Solutions
32. $y'' - 4y' + 5y = 0$
$\{e^{2x} \sin x, e^{2x} \cos x\}$
